New algorithms exploit data's strong convexity for fast linear convergence without explicit regularization.
problem Empirical risk minimization with convex loss functions.
method Primal-dual first-order algorithms that exploit data's strong convexity.
result Adaptive primal-dual algorithms achieve linear convergence without explicit regularization.
Accelerates machine learning algorithms for sparse data.
problem Efficiently solving composite convex minimization problems.
method Accelerated dual-averaging primal-dual method for composite convex minimization.
result Demonstrates advantages in handling sparse data both theoretically and empirically.
Dual PC algorithm improves structure learning of Bayesian networks.
problem Learning the structure of Bayesian networks from observational data.
method Dual PC algorithm, leveraging covariance and precision matrices, and partial correlations.
result The dual PC algorithm outperforms the classic PC algorithm in structure recovery, even with non-Gaussian data.
Dual IHT algorithm solves NP-hard non-convex sparse minimization problems.
problem Non-convex sparse minimization with ℓ 2 \ell_2 ℓ 2 -regularized loss function. method Developed a dual IHT algorithm for maximizing the non-smooth dual objective.
result Sparse recovery performance is invariant to RIP, superior to primal IHT algorithms.
Efficient algorithm solves best subset selection problem.
problem Sparse learning problems, especially best subset selection.
method Primal-dual method based on dual forms of ℓ 0 \ell_0 ℓ 0 -regularized problems. result Improves solutions of best subset selection with reduced redundant computation.
Paper develops Byzantine-resilient algorithms for decentralized learning.
problem Vulnerability of distributed learning to Byzantine attacks.
method Dual approach for decentralized optimization.
result Convergence guarantees and experimental validation of the proposed algorithm.
Optimizes subset selection in sparse learning problems.
problem Sparse learning problems, particularly best subset selection.
method Developed an efficient primal-dual algorithm leveraging dual range estimation and incremental strategy.
result Improves solutions of best subset selection with reduced redundant computation.
PDCA algorithm learns policies for RL with constraints using a primal-dual approach.
problem Offline constrained reinforcement learning with general function approximation.
method Primal-Dual-Critic Algorithm (PDCA) using a primal-dual approach.
result PDCA finds a near saddle point of the Lagrangian, nearly optimal for constrained RL.
The paper extends NUP representations to factor graphs for better estimation.
problem Nontrivial model-based estimation problems.
method Augmenting factor graphs with convex-dual variables and NUP representations; proposing a new iterative algorithm.
result A new dual algorithm for state space problems.
New algorithms solve convex-concave problems faster than previous methods.
problem Solving min-max problems without bilinear structure.
method Stochastic primal-dual algorithms with logarithmic dual updates.
result Faster convergence rates than O ( 1 / T ) O(1/\sqrt{T}) O ( 1/ T ) for certain problems. New dual approach for hedging Bermudan options efficiently.
problem Computing efficient hedging portfolios for Bermudan options.
method Pure dual approach, rewriting dual pricing formula as excess reward representation, strict convexification, Monte Carlo method.
result Convergence and effectiveness of the new algorithm tested on various Bermudan options.
Dual-based algorithms optimize distributed convex problems over networks.
problem Optimizing distributed convex problems over network constraints.
method Dual formulation of primal problem, distributed algorithms achieving optimal rates.
result Achieves optimal rates similar to centralized algorithms with additional cost related to network spectral properties.
New algorithm minimizes sum of three functions with linear operator.
problem Minimizing the sum of three convex functions with a linear operator.
method Proposes a new primal-dual algorithm for the problem.
result Proves convergence and provides convergence rates.
A simpler edge-based discretization method without dual volumes.
problem Efficiently computing edge-based discretization vectors without forming dual volumes.
method Directly compute edge-midpoint vectors and reduce dual volume formation.
result Significant reduction in computing time for tetrahedral grids.
New algorithms improve computation of optimal transport and Wasserstein barycenter.
problem Computing optimal transport and Wasserstein barycenter for multiple probability distributions.
method Introduced APDRCD and APDGCD algorithms for efficient computation, demonstrating better performance than existing methods.
result New algorithms match or exceed the best known complexities for OT problems and improve practical performance.
Unified algorithm solves convex optimization problems with optimal rates.
problem Solving nonsmooth constrained convex optimization problems.
method Unified randomized block-coordinate primal-dual algorithm.
result Achieves optimal convergence rates of O ( n / k ) \mathcal{O}(n/k) O ( n / k ) and O ( n 2 / k 2 ) \mathcal{O}(n^2/k^2) O ( n 2 / k 2 ) . We develop a primal dual active set with continuation algorithm for solving the \ell^0-regularized least-squares problem that frequently arises in compressed sensing. The algorithm couples the the primal dual active set method with a continuation strategy on the regularization parameter. At each inner iteration, it fir…
We develop polynomial time algorithms for dual volume sampling.
problem Lack of polynomial time algorithms for dual volume sampling.
method Developed exact and derandomized polynomial time sampling algorithms.
result Dual volume sampling satisfies the Strong Rayleigh property, enabling fast mixing Markov chains.
The paper explores dual learning, a technique that improves machine translation and image transformation.
problem Understanding and improving dual learning's effectiveness and conditions.
method Theoretical analysis and algorithmic extension of dual learning.
result Multi-step dual learning boosts performance under mild conditions.
New algorithm reduces big data processing time by sketching and random projection.
problem Efficiently processing large and high-dimensional data sets.
method Developed a new algorithm combining sketching and dual random projection, using preconditioned conjugate gradient.
result The algorithm can recover the optimum of the original problem up to arbitrary precision with a logarithmic number of small-scale solver calls.
Paper proposes a novel metric learning algorithm using Riemannian optimization.
problem Optimizing a smooth, convex function in Riemannian space with constraints.
method Developed a primal-dual algorithm with proximal operator for iterative optimization.
result Demonstrated the efficacy of the proposed metric learning algorithm on fund selection.
Given a convex optimization problem and its dual, there are many possible first-order algorithms. In this paper, we show the equivalence between mirror descent algorithms and algorithms generalizing the conditional gradient method. This is done through convex duality, and implies notably that for certain problems, such…
New algorithm for federated learning with non-smooth regularizers.
problem Federated Learning with non-smooth composite optimization problems.
method Proposed Federated Dual Averaging (FedDualAvg) algorithm to overcome convergence issues.
result FedDualAvg outperforms other algorithms in federated composite optimization.
Dual SVM training with budget constraint for faster accuracy.
problem Efficient support vector machine training with limited resources.
method Dual subspace ascent algorithm with budget constraint.
result Significant speed-up over primal budget training methods.
New dual formulation reduces generalization error for ERM-fDR.
problem Generalization error in constrained optimization problems.
method Introduces a dual formulation of ERM-fDR using Legendre-Fenchel transform and implicit function theorem.
result Explicit characterizations of generalization error for algorithms under mild conditions.
New algorithm achieves sublinear regret in CMDPs without error cancellations.
problem Safety constraints in reinforcement learning with error cancellations.
method Model-based primal-dual algorithm for CMDPs with multiple constraints.
result Achieves sublinear regret without error cancellations.
We propose an efficient algorithm for sparse signal reconstruction problems. The proposed algorithm is an augmented Lagrangian method based on the dual sparse reconstruction problem. It is efficient when the number of unknown variables is much larger than the number of observations because of the dual formulation. More…
Develops an online dual coordinate ascent algorithm for streaming data.
problem Lack of scalability and online adaptability in existing dual coordinate ascent algorithms.
method Introduces an online dual coordinate ascent (O-DCA) algorithm that can handle streaming data without revisiting past data.
result The O-DCA algorithm enables continuous adaptation and learning for online learning scenarios.
We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our main analysis technique provides a fresh perspective on Nesterov's excessive gap te…
A new method for SSMF improves upon existing algorithms.
problem Identify identifiable solutions in simplex-structured matrix factorization.
method Dual simplex volume maximization approach.
result The proposed method outperforms state-of-the-art SSMF algorithms.
In this paper we introduce and study the concept of optimal and surely optimal dual martingales in the context of dual valuation of Bermudan options, and outline the development of new algorithms in this context. We provide a characterization theorem, a theorem which gives conditions for a martingale to be surely optim…
Proposes a new tensor completion method using dual framework and Riemannian optimization.
problem Low-rank tensor completion with sparse or non-sparse tensor combinations.
method Dual framework, latent trace norm, Riemannian optimization, trust region algorithm.
result Shows the optimal solution lies on a Cartesian product of Riemannian manifolds.
Recently, considerable research efforts have been devoted to the design of methods to learn from data overcomplete dictionaries for sparse coding. However, learned dictionaries require the solution of an optimization problem for coding new data. In order to overcome this drawback, we propose an algorithm aimed at learn…
Improved first-order algorithm for entropy regularized OT with faster convergence.
problem Solving entropy regularized optimal transport efficiently.
method Accelerated primal-dual stochastic mirror descent algorithm with variance reduction.
result Improved rate from O ~ ( n 2.5 / ε ) \widetilde{O}({n^{2.5}}/ε) O ( n 2.5 / ε ) to O ~ ( n 2 / ε ) \widetilde{O}({n^2}/ε) O ( n 2 / ε ) . A new algorithm screens negligible components to efficiently approximate optimal transport distances.
problem Efficiently approximating the Sinkhorn distance between discrete measures.
method Screening of negligible components in the dual solution of the regularized Sinkhorn problem.
result Screenkhorn algorithm provides provable guarantees with smaller computational complexity.
A new method for faster optimization on statistical manifolds.
problem Slow convergence of first-order methods in manifold optimization.
method Dual Riemannian Newton method on manifolds with dual connections.
result Local quadratic convergence of the dual Riemannian Newton method.
Paper introduces SGA for barycenter optimization in optimal transport.
problem Optimizing Wasserstein barycenter for discrete distributions.
method Sobolev gradient ascent algorithm tailored to Wasserstein geometry.
result SGA achieves convergence rate similar to subgradient descent.
Dual memory improves reinforcement learning efficiency.
problem Training inefficiency in reinforcement learning.
method Introduces a dual memory structure with a main and cache memory.
result Dual memory structure leads to higher scores in reinforcement learning environments.
Efficient federated algorithm for calculating transportation barycenter.
problem Efficiently calculating the free-support transportation barycenter in a federated setting.
method Single-loop dual decomposition algorithm that uses only aggregated information.
result Significantly scalable and low-complexity algorithm for federated computation.
Algorithm optimizes constrained reinforcement learning with dual variables.
problem Minimizing convex functional subject to convex constraint in large state spaces.
method VPDPO algorithm using Lagrangian and Fenchel duality.
result Achieves sublinear regret and constraint violation, globally optimal policy.
PURE-CD algorithm proves complexity bounds for convex-concave problems.
problem Solving convex-concave min-max problems with bilinear coupling.
method Primal-dual algorithm with random extrapolation and coordinate descent (PURE-CD).
result Complexity bounds match or improve existing results for dense and sparse problems.
New algorithm selects robust martingale for optimal stopping problems.
problem Optimal stopping problems in stochastic processes.
method Randomized dual martingale minimization algorithm.
result Efficiently selects Doob martingale as close as possible.
In this paper, we consider the problem of recovering a sparse signal based on penalized least squares formulations. We develop a novel algorithm of primal-dual active set type for a class of nonconvex sparsity-promoting penalties, including ℓ 0 \ell^0 ℓ 0 , bridge, smoothly clipped absolute deviation, capped ℓ 1 \ell^1 ℓ 1 and mini…
We present DUAL-LOCO, a communication-efficient algorithm for distributed statistical estimation. DUAL-LOCO assumes that the data is distributed according to the features rather than the samples. It requires only a single round of communication where low-dimensional random projections are used to approximate the depend…
DualIV simplifies non-linear IV regression via dual formulation.
problem Non-linear instrumental variable regression with potential first-stage regression bottleneck.
method Dual formulation of non-linear IV regression as a convex-concave saddle-point problem, leading to a kernel-based algorithm with analytic solution.
result Empirical results show competitive performance compared to existing algorithms.
LEAD algorithm speeds up decentralized optimization with compression.
problem Slow convergence and stability issues in decentralized optimization with compression.
method Proposes the first linearly convergent decentralized algorithm with compression.
result First consensus error bound for coupled dynamics of primal and dual updates.
A new GAN algorithm using primal-dual formulations of optimal transport.
problem Building latent variable models of data distributions.
method Primal formulation for inference and dual formulation for adversarial training.
result Improves mode coverage and avoids averaging properties of auto-encoding models.
A new method for non-negative matrix factorization using generalized dual divergence.
problem Non-negative matrix factorization for various noise structures.
method Theoretical framework based on generalized dual Kullback-Leibler divergence, with algorithms developed and proven convergence using Expectation-Maximization.
result Generalizes existing methods and provides an alternative for non-negative matrix factorizations.